Classical large deviation theorems on complete Riemannian manifolds

Richard C. Kraaij, Frank Redig*, Rik Versendaal

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
79 Downloads (Pure)


We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton–Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The approach also provides a new proof of Schilder's theorem. Additionally, we provide a proof of Schilder's theorem by using an embedding into Euclidean space, together with Freidlin–Wentzell theory.

Original languageEnglish
Pages (from-to)4294-4334
Number of pages41
JournalStochastic Processes and their Applications
Issue number11
Publication statusPublished - 2019

Bibliographical note

Accepted author manuscript


  • Cramér's theorem
  • Geodesic random walks
  • Hamilton–Jacobi equation
  • Large deviations
  • Non-linear semigroup method
  • Riemannian Brownian motion


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